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Labour Economics

VIEWS: 16 PAGES: 22

									Labour Economics

   Dr Hamish Low
      Lecture 2
  Outline: Labour Supply (cont)
• Explaining hours of work / participation

• Life-cycle model of labour supply

• Uncertainty

• Hours of work may affect wage rate
Explaining Hours of work

     Increase in wage rate
y
                             •Substitution effect
             B                        (relative price has
    A’                                changed – leisure is
         A                            more expensive)

                             •Income effect
                                     (income has increased)
                        l
                   H
Slutsky Equation:

  z w, p, m  z c w, p, u  z w, p, m 
                                            H  z 
       w             w            m

      ??               Hicksian
                                                       + ve
                      Substitutio
                                                   (normal good)
                       n Effect
                         - ve

     Need estimates of SE and IE
     specifically, estimates of income elasticity of labour supply and the
     compensated wage elasticity.
         ln h   0  1 ln w

           2 ln other income 

           3 ( no kids)

What data to use?
       Variation in wages across individuals?
       Variation over time for the same individual?


Two problems:
      1. what does it mean to say “a wage increase”
      2. hours of work may affect the wage rate
What does it mean to say “a wage increase”

• Static model: opportunity set has
  expanded.

• Life-cycle context:
  – wage has increased along expected trajectory
  – wage is higher than expected
             Life-cycle Wages
Log [wage]


  2.25

      2

  1.75

   1.5

  1.25

      1

             30   40    50         60
                             Age
• Anticipated change in wage with age
  – increase in wage generates intertemporal substitution
    in hours worked
  – wealth does not change
• Unanticipated permanent change in wage
  – increase in wage increases lifetime wealth
  – no incentive to intertemporally substitute
• Unanticipated temporary change in wage
  – increase in wage makes little difference to wealth
  – incentive for intertemporal substitution


• Distinguish change in labour supply following
  wage change from labour supply ex ante.
              c1   z1 
    max     t
                                  s.t. At 1  R At  wt H  zt   ct 
        t 1 1   1  
              t  c1   z1        At 1                          
L  max                     t        At  wt H  zt   ct  
        t 1    1   1           R                              

            L t                   L t 
                :  ct  t              :  zt  t wt
            ct                      zt


                       L       
                             :  t  t 1  0
                      At 1    R



                                                 
                                   z         z
                                t t   t 1 t 1
                                  wt R        wt 1
                                     
                 z         z
              t t   t 1 t 1
                wt R        wt 1


                         
               zt                  wt
              
              z             R
               t 1                wt 1



  ln zt  ln zt 1   ln R   ln wt  ln wt 1 




                                   ln R  
                               1                1
                ln zt 1                           ln wt 1
                                               
                                                                   1
                                                      High EIS :
                                                                   
    2.25

        2
                         1                                             Log [wage]
             Low EIS :
    1.75                 

     1.5

    1.25

        1

                         30           40               50                 60
                                                            Age
      • Choice of when to work in life-cycle reflects willingness
      and ability to substitute hours of work intertemporally

      • Evolutionary or Frisch elasticities

Estimation
                ln ht 1   0  1 ln R    2  ln wt 1   t 1

               (holding marginal utility of wealth constant)
    2.25

        2    Actual hours of work

                                                             Log [wage]
    1.75

      1.5

    1.25

        1

                       30           40           50             60
                                                       Age


• Hard to explain the downturn in hours after age 50
 Implications for consumption

Are consumption and hours of work substitutes or complements?

        So far have assumed additive separability

        Substitutes: consumption is low when hours of work are high
                 (no leisure time to enjoy earnings?)

        Complements: consumption is high when hours of work are high
               (have to spend more to make the most of few hours of
               leisure!)


      u c, h                     2u c, h 
                                               0   Substitutes
                                    ch
      u c, h 
                                   2u c, h 
        c                                     0   Complements
                                    ch
Implications for consumption




 2.25
            Log [Consumption] (Subst)
    2
          Hours of work
 1.75

  1.5
                          Log [Consumption] (Compl)
 1.25
            Log [wage]
    1

                30            40                50              60
                                                     Age

                                        Heckman American Economic Review (1974)
    2.25
                                                Actual Log [consumption]
        2    Actual hours of work

                                                             Log [wage]
    1.75

      1.5

    1.25

        1

                       30           40           50             60
                                                       Age

• Hard to explain the downturn in hours after age 50

• What does this imply for hours and consumption being substitutes?
                     Uncertainty

• unexpected changes to wages: may be
  permanent or transitory

  – permanent: large wealth effect, small opportunity for
    intertemporal substitution

  – transitory: small wealth effect, large opportunity for
    intertemporal substitution


• Bush’s tax cuts: temporary or permanent?
                          c1   z1  
            max E0   t                           s.t. At 1  R At  wt H  zt   ct 
                    t 1 1   1   


                                                  1 
 Et  ln zt 1   ln R   Et  ln wt 1        var ln zt 1   var ln wt 1 
                  1               1                                      1
                                                  2                    
• Expected change in hours of leisure depends on expected wage growth
  and on uncertainty about wages

• Realised change in hours of leisure also depends on realisations of wage
  shocks

• Parametric vs evolutionary changes in wages


     Estimation
                         ln ht 1   0  1 ln R    2  ln wt 1   t 1

            2 contains both the Frisch elasticity and the parametric shift in the wage profile.
Log [wage]


  2.25

      2

  1.75

   1.5

  1.25

      1

                 30         40         50          60
                                            Age




  Increase in hours associated with temporary cut in tax rate

  Decrease in hours associated with permanent tax cut
Uncertainty means work harder when young, but also defer
consumption until old.

   hours                                               ln ct , ln wt H
   of work
                  hours of work
     2000                                                   11.0

                 ln wt H
     1500                                                   10.5

                       ln ct
     1000                                                   10.0

      500                                                   9.0


                  30              40         50   60
                                       Age
Hours of work may affect the wage rate

• High wage rate when old is only realised
  because of hours worked when young
   – no option to defer work until wage rises

• On-the-job learning (and depreciation when
  unemployed)

• Implications for helping get individuals back into
  labour force
   – (Working Tax Credit, Earned Income Tax Credit)
                  Conclusions
• Life-cycle model of labour supply
  – work when wages are high
  – key parameter is Intertemporal Elasticity of Substitution
  – need care in interpreting static estimates of elasticities


• Uncertainty over wages
  – transitory vs permanent wage shocks


• Returns to experience
  – wage is affected by hours of work / participation (careful
    in regression analysis)
                Precautionary Motive
u ct , zt 
   ct


E MUt c 
MUt E[c]

                  c                      c           ct
                          E[c]
 So, greater uncertainty increases expected marginal utility.

 This induces a shift of resources to the future (when expected
 marginal utility is high)

								
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